In the manufacture of heat exchanger cores such as motor vehicle radiators, it is common practice to employ channel shaped reinforcement members that sandwich alternately arranged oval tubes and air centers and contact at their ends with headers that receive opposite ends of the tubes. Processing straps are then wrapped about the thus formed core assembly so that the reinforcements apply a clamping load to hold the assembly tightly together for brazing in addition to later serving to protect the sides of the core as well as reinforce same. While this manner of construction has proven generally satisfactory, there remains the need for continuous improvement, particularly where the core and straps are of different material (e.g. aluminum and steel, respectively), and special reinforcements (and thus added tooling costs) are required to compensate for the differences in thermal expansion during brazing and/or usage. Moreover, as the core depth and thus the tube width is increased for increased performance, the outside tubes have a tendency to collapse along their long side and separate from their slots in the headers, thus resulting in leaks.